New Insights into the RLS Algorithm

The recursive least squares (RLS) algorithm is one of the most popular adaptive algorithms that can be found in the literature, due to the fact that it is easily and exactly derived from the normal equations. In this paper, we give another interpretation of the RLS algorithm and show the importance of linear interpolation error energies in the RLS structure. We also give a very efficient way to recursively estimate the condition number of the input signal covariance matrix thanks to fast versions of the RLS algorithm. Finally, we quantify the misalignment of the RLS algorithm with respect to the condition number.

[1]  Jacob Benesty,et al.  Adaptive Signal Processing: Applications to Real-World Problems , 2003 .

[2]  S. Thomas Alexander,et al.  Adaptive Signal Processing , 1986, Texts and Monographs in Computer Science.

[3]  Bernard C. Picinbono,et al.  Some properties of prediction and interpolation errors , 1988, IEEE Trans. Acoust. Speech Signal Process..

[4]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[5]  T. Kailath,et al.  A state-space approach to adaptive RLS filtering , 1994, IEEE Signal Processing Magazine.

[6]  Steven Kay,et al.  Some results in linear interpolation theory , 1983 .

[7]  Maurice Bellanger,et al.  Adaptive digital filters and signal analysis , 1987 .